= Area enclosed by two chords and a circular arc
{title2=$A=R^2(\theta+\sin\theta)$}
Take a <circle> of <radius> $R$, a vertex $A$ on its circumference, and two chords from $A$ symmetric about the diameter through $A$. If their <angle> is $0\leq\theta\leq\pi$, choose the arc between their other endpoints that does not contain $A$. The <area> bounded by the two chords and that arc is $R^2(\theta+\sin\theta)$. To calculate it, set $A=(0,R)$ and the other endpoints to $(\pm R\sin\theta,-R\cos\theta)$. Their <triangle> has area $R^2\sin\theta(1+\cos\theta)$, and the adjoining <circular segment>, of central <angle> $2\theta$, has area $R^2(\theta-\sin\theta\cos\theta)$. The sum gives the formula, including the limiting zero-area and full-disk cases.
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